Gold Seal Lesson:
Where Are We

Copernicus Education Gateway

Subject:

Science

Grade:

9-12

ICLE Standards:

Mathematics: Apply trigonometry to problem situations involving triangles.

Science: Develop an understanding of science as a human endeavor.

Performance Task:

Anna Maria joined the Navy after high school and became a navigator on a destroyer. As part of her duties, she has to plot the position of her ship at sea and determine its correct course for the Captain. This activity provides you with some of the mathematical knowledge to find distances that can be represented as a side of a right triangle. You will first construct a sextant, an instrument that can be used to measure angles, and then use the sextant to find the degree measure of an acute angle in a right triangle. Using the tangent ratio, you will then be able to find the height of an object that cannot be measured directly.

Materials Needed:

• protractor

• transparent tape or glue

• drinking straw

• string (6")

• cardboard square (6" by 6")

• meter tape

• bullet fishing weights or washers

Construct a sextant according the diagram.

1. Make a large knot in one end of the 6" string and run the string through the bullet weight or washers.

2. Tie the opposite end of the string to the flat side of the protractor.

3. Lay the protractor on the 6" x 6" cardboard upside down with the flat side flush with the top edge of the cardboard, making sure the string can swing freely from its points of attachment. Attach the protractor with tape. Mount the drinking straw on the top edge of the cardboard.

Use the following procedure for finding the height of an object.

1. With your partner select a tall object to measure and decide who will be the sextant user and who will be the recorder.

2. Measure and record the height from the floor to the eye of the sextant user.

3. The sextant user stands a distance from the object and sights the top of the object through the straw.

4. The recorder reads the acute angle on the protractor created by the string.

5. Obtain and record the measure of the sighting angle by subtracting the reading in #4 from 90 degrees.

6. The recorder measures and records the distance from the position of the user to the base of the object using a meter tape.

7. Find the height of the object above eye level using the tangent ratio.

8. Find the total height of the object.

9. Research methods on how mariners used celestial bodies to navigate the Earth's oceans and write a paper describing these methods.

Optional:
Compare the mariners' methods with methods used by the Global Positioning System today.

Note to the teacher: Students should work in pairs on this activity, which may be used to integrate trigonometry with earth and physical science. Although the task is more aligned with mathematics learning, the learning in the task has much application in the sciences and in the real world. Upon completing the activity, students should have an understanding of how to use the tangent ratio to find the height of objects and how ancient mariners used trigonometry to plot their positions and courses at sea.

Knowledge / Skills:

Perform operations with signed (positive and negative) numbers, including decimals, ratios, percents, and fractions.  (m1)

Understand the angle relationships in triangles (i.e., acute, obtuse, right, interior, and exterior).  (m14)

Use the Pythagorean theorem to compute side lengths of right triangles.  (m21)

Use the technique of dimensional analysis to convert units of measure (e.g., convert km/hr to m/min).  (m33)

Understand the concepts of right triangle trigonometry and solve right triangles using basic trigonometric ratios (sine, cosine, tangent).  (m57)

Plan and apply real or hypothetical models and constructions to facilitate investigation and learning and the solution to practical problems.  (xs2)

Gather information from a variety of sources, including electronic sources, and summarize, analyze, and evaluate its use for a report.  (ela3)

Use expository writing skills in subjects other than English language arts.  (ela58)

Rubric:

(Material in parentheses refers to the optional part of the task.)

3 Points  =  The student can construct a sextant and use it properly. He/she is able to follow directions and use the tangent ratio to find the height of an object. The student demonstrates an ability to use research methods and his/her paper clearly and thoroughly describes methods used by mariners to use celestial bodies to navigate the Earth's oceans. (The student gives a good comparison of these methods with the methods used by the Global Position System today.)

2 Points  =  The student needs some assistance in constructing the sextant and using it properly. He/she finds it difficult to follow directions, but is able with help to use the tangent ratio to find the height of an object. The student demonstrates adequate research skills and his/her paper gives an acceptable description of methods used by mariners to use celestial bodies to navigate the Earth's oceans. (The student gives a fair comparison of these methods with the methods used by the Global Position System today.)

1 Point  =  The student does not complete the activity. Even with assistance, the sextant is poorly constructed and not very accurate. The student was not able to use the tangent ratio to find the height of the chosen object. The student's research is sketchy, vague, and does not give an adequate description of how mariners used celestial bodies to navigate the Earth's oceans. (The student is unable to compare these methods with the methods used by the Global Position System today.)

0 Points  =  The student does not complete the activity and displays little effort. No understanding of how the tangent ratio can be used to find the height of an object is evident. The student does not do the necessary research and gives no description of how mariners used celestial bodies to navigate the Earth's oceans. (No attempt is made to compare those methods with the methods used by the Global Position System today.)

Keywords:

EARTH SCIENCE
OCEANS
STARS
PLANETS
SEXTANT
RIGHT ANGLES
PROBLEM SOLVING

Grades:

Kg [] - 1 [] - 2 [] - 3 [] - 4 [] - 5 [] - 6 [] - 7 [] - 8 [] - 9 [X] - 10 [X] - 11 [X] - 12 [X]

ICLE Application:

D

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